SAGMAN: Stability Analysis of Graph Neural Networks on the Manifolds
CoRR(2024)
摘要
Modern graph neural networks (GNNs) can be sensitive to changes in the input
graph structure and node features, potentially resulting in unpredictable
behavior and degraded performance. In this work, we introduce a spectral
framework known as SAGMAN for examining the stability of GNNs. This framework
assesses the distance distortions that arise from the nonlinear mappings of
GNNs between the input and output manifolds: when two nearby nodes on the input
manifold are mapped (through a GNN model) to two distant ones on the output
manifold, it implies a large distance distortion and thus a poor GNN stability.
We propose a distance-preserving graph dimension reduction (GDR) approach that
utilizes spectral graph embedding and probabilistic graphical models (PGMs) to
create low-dimensional input/output graph-based manifolds for meaningful
stability analysis. Our empirical evaluations show that SAGMAN effectively
assesses the stability of each node when subjected to various edge or feature
perturbations, offering a scalable approach for evaluating the stability of
GNNs, extending to applications within recommendation systems. Furthermore, we
illustrate its utility in downstream tasks, notably in enhancing GNN stability
and facilitating adversarial targeted attacks.
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